Explicit formula for a fundamental class of functions. (English) Zbl 1210.11097

Avdispahić, Muharem; Smajlović, Lejla

Bull. Belg. Math. Soc. - Simon Stevin 12, No. 4, 569-587 (2005).

Summary: The purpose of this paper is to prove an analogue of A. Weil’s explicit formula for a fundamental class of functions, i.e., the class of meromorphic functions that have an Euler sum representation and satisfy certain a functional equation. The advance of this explicit formula is that it enlarges the class of allowed test functions, from the class of functions with bounded Jordan variation to the class of functions of \(\phi \)-bounded variation. A condition posed to the test function at zero is also reconsidered.

MSC:

11M36	Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
26A45	Functions of bounded variation, generalizations
42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords:

explicit formula; \(\phi\)-variation; Weil’s functional